As mentioned in [1]}, it is not unreasonable to ask why we need two methods - the HP and GIT, which are used to solve the same problem and demonstrate the same performance. The answer is interesting. As shown in [2]}, the GIT method produces very accurate results at high strikes and maturities (i.e., when the option price is relatively small), in contrast to the HP method, which struggles under these circumstances. One can verify this fact by looking at the exponents under the GIT solution integral proportional to the time \(\tau \) . Contrary, when the price is higher (short maturities, low strikes), the GIT method is slightly less accurate than the HP method since the exponents in the HP solution integral are inversely proportional to \(\tau \) .
